If 5√5x³ + 2√2y³ = (Ax + √2y)(Bx² + 2y² + Cxy), then the value of (A² + B² - C²) is:

Solution (By Examveda Team)

$$\eqalign{ & 5\sqrt 5 {x^3} + 2\sqrt 2 {y^3} = \left( {Ax + \sqrt 2 y} \right)\left( {B{x^2} + 2{y^2} + Cxy} \right) \cr & {\left( {\sqrt 5 x} \right)^3} + {\left( {\sqrt 2 y} \right)^3} = \left( {\sqrt 5 x + \sqrt 3 y} \right)\left( {5{x^2} + 9{y^2} - \sqrt {10} xy} \right) \cr & \left( {\sqrt 5 x + \sqrt 3 y} \right)\left( {5{x^2} + 9{y^2} - \sqrt {10} xy} \right) = \left( {Ax + \sqrt 2 y} \right)\left( {B{x^2} + 2{y^2} + Cxy} \right) \cr & {\text{Comparison both side:}} \cr & A = \sqrt 5 \cr & B = 5 \cr & C = - \sqrt {10} \cr & {A^2} + {B^2} + {C^2} = 5 + 25 - 10 = 20 \cr} $$